Finite Group Databasebeta

← #16835516

Subgroups — #16835516

Order 3712.

378 conjugacy classes of subgroups; only the 70 normal subgroups are shown.

normal subgroups only

This group has 378 conjugacy classes of subgroups — too many to draw. Only its 70 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11745345C211yesmaximal, characteristic, complemented
2C2×#11745215C212yesmaximal
3#14272106C211yesmaximal, characteristic, complemented
4#14272041C212yesmaximal, complemented
5C2×#11745256C211yesmaximal, characteristic
6C22×D116C2211yescharacteristic
7C22×C4×D29C2211yescharacteristic
8C2×C22⋊#1181C2212yes—
9C2×C22⋊#1181C2212yes—
10#11745345—24no—
11C2×C4⋊#1181—21no—
12C2×C4×#1181—21no—
13C2×C4⋊C4×C29C411yescharacteristic, complemented
14C2×#90781C411yescharacteristic, complemented
15C2×#90781C411yescharacteristic, complemented
16C2×#90781C2211yescharacteristic
17C2×#90779C411yescharacteristic, complemented
18#11745256—21no—
19#11745256—21no—
20#11745256—21no—
21#11745256—21no—
22(C2×#1181)⋊C4—21no—
23(C2×#1181)⋊C4—21no—
24#11745215—24no—
25C23×D29C2×C411yescharacteristic
26C23×D29C2311yescharacteristic
27C22×#1181—22no—
28C22×#1181—22no—
29C22×C4×C29C2×C411yescharacteristic
30C22×C4×C29C2×C411yescharacteristic
31C22×C4×C29C2×C411yescharacteristic
32C22×Dic29C2×C411yescharacteristic
33C22×Dic29C2×C411yescharacteristic
34C2×D116—22no—
35C2×D116—21no—
36C2×D116—21no—
37C2×D116—22no—
38C2×C4×D29—22no—
39C2×C4×D29—22no—
40C2×C4×D29D411yescharacteristic
41C2×C4×D29D411yescharacteristic
42C2×C4×D29D411yescharacteristic
43C2×C4×D29D411yescharacteristic
44C22⋊#1181—22no—
45C22⋊#1181—22no—
46C22⋊#1181—22no—
47C22⋊#1181D414yes—
48C4⋊#1181—24no—
49C4×#1181—24no—
50C4⋊C4×C29—21no—
51C4⋊C4×C29—21no—
52#90781—21no—
53#90781—21no—
54#90781—21no—
55#90781—21no—
56#90781—21no—
57#90781—21no—
58#90779—21no—
59#90779—21no—
60C23×C29C22×C411yescharacteristic
61C22×D29—21no—
62C22×D29—22no—
63C22×D29—41no—
64C22×D29—41no—
65C22×D29—41no—
66C22×D29—41no—
67C22×D29C2×D411yescharacteristic
68C22×D29C2×D411yescharacteristic
69C22×D29C2×D412yes—
70C22×D29#4112yes—
71C2×#1181—24no—
72C2×#1181—42no—
73C2×#1181—42no—
74C2×#1181—42no—
75C2×#1181—42no—
76C2×#1181—42no—
77C2×C4×C29—22no—
78C2×C4×C29—21no—
79C2×C4×C29—21no—
80C2×C4×C29—22no—
81C2×C4×C29—41no—
82C2×C4×C29C22⋊C411yescharacteristic
83C2×C4×C29C22⋊C411yescharacteristic
84C2×Dic29—22no—
85C2×Dic29—21no—
86C2×Dic29—41no—
87C2×Dic29C22⋊C411yescharacteristic
88C2×Dic29C22⋊C411yescharacteristic
89D116—41no—
90D116—42no—
91D116—41no—
92C4×D29—21no—
93C4×D29—21no—
94C4×D29—22no—
95C4×D29—22no—
96C4×D29—21no—
97C4×D29—21no—
98#1899—291nomaximal, Sylow
99C22×C29—21no—
100C22×C29—21no—
101C22×C29C2×C22⋊C411yescharacteristic
102C22×C29C4×D412yes—
103C2×D29—21no—
104C2×D29—21no—
105C2×D29—21no—
106C2×D29—21no—
107C2×D29—42no—
108C2×D29—42no—
109C2×D29—41no—
110C2×D29—41no—
111C2×D29—41no—
112C2×D29—82no—
113C2×D29#12011yescharacteristic
114C2×D29#12112yes—
115C2×D29#12311yescharacteristic
116#1181—44no—
117#1181—82no—
118C4×C29—21no—
119C4×C29—21no—
120C4×C29—41no—
121C4×C29—41no—
122Dic29—21no—
123Dic29—21no—
124Dic29—41no—
125C2×#123—291no—
126C2×#117—291no—
127C2×#99—292no—
128#381—291no—
129#342—292no—
130C2×C29—22no—
131C2×C29#38611yescharacteristic
132C2×C29#41011yescharacteristic
133C2×C29#41011yescharacteristic
134D29—21no—
135D29—22no—
136D29—21no—
137D29—81no—
138C22×D4—291no—
139C23×C4—291no—
140#123—581no—
141#123—581no—
142#123—581no—
143#123—581no—
144#117—584no—
145C2×C4⋊C4—291no—
146C2×C4⋊C4—581no—
147C2×C4⋊C4#118111yescharacteristic, complemented
148C2×C22⋊C4—292no—
149C2×C22⋊C4—291no—
150C2×C22⋊C4—291no—
151C2×C22⋊C4—291no—
152C2×C22⋊C4—292no—
153C2×C42—581no—
154#99—584no—
155#95—581no—
156#95—581no—
157C29#189911yescharacteristic, complemented, Sylow
158C24—291no—
159C24—291no—
160C2×D4—582no—
161C2×D4—581no—
162C2×D4—581no—
163C2×D4—582no—
164C22×C4—291no—
165C22×C4—291no—
166C22×C4—291no—
167C22×C4—291no—
168C22×C4—291no—
169C22×C4—291no—
170C22×C4—582no—
171C22×C4—582no—
172C22×C4—582no—
173C22×C4—582no—
174C22×C4C2×#118111yescharacteristic
175C22×C4C2×#118111yescharacteristic
176C22×C4C2×#118111yescharacteristic
177C4⋊C4—21no—
178C4⋊C4—21no—
179C4⋊C4—581no—
180C4⋊C4—581no—
181C4⋊C4—584no—
182C22⋊C4—294no—
183C22⋊C4—581no—
184C22⋊C4—581no—
185C22⋊C4—581no—
186C22⋊C4—581no—
187C22⋊C4—582no—
188C22⋊C4—581no—
189C22⋊C4—581no—
190C22⋊C4—582no—
191C22⋊C4—582no—
192C42—584no—
193C23—291no—
194C23—291no—
195C23—292no—
196C23—292no—
197C23—581no—
198C23—582no—
199C23—1161no—
200C23—1161no—
201C23—1161no—
202C23—1161no—
203C23C22×#118111yescharacteristic
204D4—1161no—
205D4—1162no—
206D4—1161no—
207C2×C4—22no—
208C2×C4—22no—
209C2×C4—21no—
210C2×C4—21no—
211C2×C4—41no—
212C2×C4—291no—
213C2×C4—291no—
214C2×C4—581no—
215C2×C4—581no—
216C2×C4—582no—
217C2×C4—582no—
218C2×C4—581no—
219C2×C4—581no—
220C2×C4—582no—
221C2×C4—584no—
222C2×C4—581no—
223C2×C4—1162no—
224C2×C4—1162no—
225C2×C4—1161no—
226C2×C4—1162no—
227C2×C4—1162no—
228C2×C4—1162no—
229C2×C4C22⋊#118111yescharacteristic
230C2×C4C22⋊#118111yescharacteristic
231C22—21no—
232C22—21no—
233C22—291no—
234C22—292no—
235C22—291no—
236C22—581no—
237C22—581no—
238C22—581no—
239C22—581no—
240C22—1162no—
241C22—1162no—
242C22—1161no—
243C22—1161no—
244C22—1161no—
245C22—2322no—
246C22D4×#118112yes—
247C22C2×C22⋊#118111yescharacteristic
248C4—21no—
249C4—21no—
250C4—41no—
251C4—41no—
252C4—581no—
253C4—581no—
254C4—1164no—
255C4—1161no—
256C4—2322no—
257C2—22no—
258C2—581no—
259C2—582no—
260C2—581no—
261C2—2321no—
262C2#1427211111yescharacteristic
263C2#1427214211yescharacteristic
264C2#1427214411yescharacteristic
subgroupG/H
centerC22C2×C22⋊#1181
commutatorC23×C29C22×C4
FrattiniC23C22×#1181
FittingC2×C4⋊C4×C29C4
socleC22×C29C2×C22⋊C4
prime radicalC22×D116C22
cosocleC23×D29C23
hypercenterC2×C4⋊C4#1181
hypocenterC29#1899
LCSG ▷ C23×C29 ▷ C2×C29 ▷ C29
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4⋊C4

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C2×#11745345C2semidirect
3. #14272106C2semidirect
4. #14272041C2semidirect
13. C2×C4⋊C4×C29C4semidirect
14. C2×#90781C4semidirect
15. C2×#90781C4semidirect
17. C2×#90779C4semidirect
147. C2×C4⋊C4#1181semidirect
157. C29#1899semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×#117453452
C2×#117452152
#142721062
#142720412
C2×#117452562
#189929